Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 11"

(Solution)
 
(15 intermediate revisions by 6 users not shown)
Line 1: Line 1:
 
== Problem ==
 
== Problem ==
 +
Find the sum of the squares of the roots, real or complex, of the system of simultaneous equations
 +
 +
<math>x+y+z=3,~x^2+y^2+z^2=3,~x^3+y^3+z^3 =3.</math>
 +
 +
==Solution==
 +
The roots are <math>x</math>, <math>y</math>, and <math>z</math>, and we add the squares:
 +
 +
<cmath>x^2+y^2+z^2=\boxed{003}</cmath>
 +
 +
==See Also==
 +
http://www.artofproblemsolving.com/Wiki/index.php/1973_USAMO_Problems/Problem_4
 +
{{Mock AIME box|year=2006-2007|n=2|num-b=10|num-a=12}}

Latest revision as of 21:55, 20 October 2019

Problem

Find the sum of the squares of the roots, real or complex, of the system of simultaneous equations

$x+y+z=3,~x^2+y^2+z^2=3,~x^3+y^3+z^3 =3.$

Solution

The roots are $x$, $y$, and $z$, and we add the squares:

\[x^2+y^2+z^2=\boxed{003}\]

See Also

http://www.artofproblemsolving.com/Wiki/index.php/1973_USAMO_Problems/Problem_4

Mock AIME 2 2006-2007 (Problems, Source)
Preceded by
Problem 10
Followed by
Problem 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15